Scala analysis: xen12-wilson-08-4C3-tetrany-04
1-3-9-15 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 5/3 884.358713 major sixth, BP sixth 3: 15/8 1088.268715 classic major seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 5/4 386.3137 major third 2: 4/3 498.0450 perfect fourth 3: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 1 5/4 386.314 cents major third 1: 1 4/3 498.045 cents perfect fourth 2: 1 6/5 315.641 cents minor third 2: 1 4/3 498.045 cents perfect fourth 2: 1 3/2 701.955 cents perfect fifth 2: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 3/2 701.955 cents perfect fifth 3: 1 8/5 813.686 cents minor sixth 3: 1 16/9 996.090 cents Pythagorean minor seventh 3: 1 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 0.0 : 386.3 884.4 1088.3 1200.0 386.3 : 498.0 702.0 813.7 1200.0 884.4 : 203.9 315.6 702.0 1200.0 1088.3: 111.7 498.0 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 498.0450 cents 5/4, 386.3137 cents 16/15, 111.7313 cents 2: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 9/10,-182.4037 cents 3: 701.9550 .. 1088.2687 cents 5/4, 386.3137 cents 9/10,-182.4037 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 4/3, 498.0450 cents Average / Smallest step : 2.685013 Largest / Average step : 1.660150 Largest / Smallest step : 4.457525 Median interval of one step : 295.11186 cents, amount: 0 Least squares average step : 340.66124 cents, oct.: 1362.64497 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : CDBA Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.663646 Lumma stability : 0.186219 Lumma impropriety factor : 0.304006 Rothenberg efficiency : 0.583333 redundancy: 0.416667 Efficiency x scale size : 2.333333 Number of different interval sizes : 10 = 3.33333 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 25/24, 70.6724 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 701.955 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 25.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 5 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.063559 Average absolute harmonicity : 0.328053 Specific harmonicity : 0.313545 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 7.200000E+02, 9.49185 octaves Euler's gradus suavitatis : 13 Sum of Mann's harmonic distance : 21.5, average 5.37500 Mersenne's string divisions : 1656 Sum of van Prooijen's expressibility: 2.57403, average 0.64351 Sum of Tenney's harmonic distance : 4.85733, average 1.21433 Vogel's harmonic complexity : 8.75000 Wille's k value : 22 Wilson's harmonic complexity : 11 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 24.35971, average 2.43597 Lattice compactness (without 2's) : 11.65685, average 1.16569 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.00000 6 1 3: -1 .. 1 0.00000 2 5: 0 .. 1 0.75000 3 3 Average exponent except 2's : 3 / 4 = 0.75000 Average absolute exponent except 2's: 5 / 4 = 1.25000 Scale is weakly epimorphic with val: <4 5 10| Scale is weakly epimorphic with val: <4 7 10|
FIT/MODE
4: 1 2 1 0 N D3 SD: 71.0257 c. M:-111.7313 c. 6: 2 2 1 1 P D3 S SD: 61.4310 c. M: 88.2687 c. 7: 2 3 1 1 N SD: 39.3476 c. M: 59.6973 c. 8: 3 3 1 1 N D3 S SD: 37.9641 c. M:-63.6863 c. 9: 3 4 1 1 N SD: 27.6246 c. M:-48.9746 c. 10: 3 4 2 1 N SD: 26.1174 c. M: 44.3587 c. 11: 4 4 2 1 N SD: 25.7257 c. M:-50.0499 c. 12: 4 5 2 1 N SD: 11.9330 c. M:-15.6413 c. 19: 6 8 3 2 N SD: 8.1700 c. M: 14.5845 c. 22: 7 9 4 2 N SD: 6.3732 c. M: 11.6314 c. 31: 10 13 5 3 N SD: 3.7256 c. M:-5.9639 c. 34: 11 14 6 3 N SD: 3.2375 c. M:-5.8489 c. 53: 17 22 9 5 N SD: 1.2204 c. M: 1.4763 c. 87: 28 36 15 8 N SD: 1.0599 c. M: 1.6001 c. 118: 38 49 20 11 N SD: 0.2143 c. M:-0.3870 c. 289: 93 120 49 27 N SD: 0.2079 c. M: 0.3794 c. 323: 104 134 55 30 N SD: 0.1599 c. M:-0.2762 c. 376: 121 156 64 35 N SD: 0.1742 c. M: 0.3162 c. 441: 142 183 75 41 N SD: 0.0926 c. M:-0.1667 c. 494: 159 205 84 46 N SD: 0.0841 c. M: 0.1482 c. 559: 180 232 95 52 N SD: 0.0790 c. M:-0.1034 c. 612: 197 254 104 57 N SD: 0.0342 c. M: 0.0450 c. 730: 235 303 124 68 N SD: 0.0284 c. M: 0.0495 c. 1171: 377 486 199 109 N SD: 0.0207 c. M:-0.0319 c. 1665: 536 691 283 155 N SD: 0.0201 c. M: 0.0344 c. 1783: 574 740 303 166 N SD: 0.0058 c. M:-0.0095 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 91.2019 cents 3:4:5 x 6 S SD: 37.2438 cents 4:5:7 x 8 SD: 28.1557 cents 7:9:12:13:14 SD: 17.7334 cents 8:10:13:15:16 SD: 10.9578 cents 9:11:15:17:18 SD: 10.2375 cents 12:15:20:23:24 SD: 9.5127 cents 15:19:25:28:30 SD: 6.0481 cents 16:20:27:30:32 SD: 5.3766 cents 24:30:40:45:48 S SD: 0.0000 cents